Correct Answer - Option 4 : x

2 + y

2 + x - 2y - 21 = 0

**CONCEPT****:**

If (x_{1}, y_{1}) and (x_{2}, y_{2}) are the end points of the diameter of a circle. Then the equation of such a circle is (x – x_{1}) ⋅ (x – x_{2}) + (y – y_{1}) (y – y_{2}) = 0

**CALCULATION****:**

Given: The end points of the diameter of a circle are A (2, - 3) and B(- 3, 5)

As we know that, if (x1, y1) and (x2, y2) are the end points of the diameter of a circle then the equation of such a circle is (x – x1) ⋅ (x – x2) + (y – y1) (y – y2) = 0

Here, x_{1} = 2, y_{1} = -3, x_{2} = -3 and y_{2} = 5

⇒ (x - 2) ⋅ (x + 3) + (y + 3) ⋅ (y - 5) = 0

⇒ x^{2} + y^{2} + x - 2y - 21 = 0

So, the equation of the required circle is: x2 + y2 + x - 2y - 21 = 0

Hence, **option D** is the correct answer.